This class covers the QR Code model 2 specification, supporting all versions (sizes) * from 1 to 40, all 4 error correction levels, and only 3 character encoding modes.
*/ public final class QrCode { /*---- Public static factory functions ----*/ /** * Returns a QR Code symbol representing the specified Unicode text string at the specified error correction level. * As a conservative upper bound, this function is guaranteed to succeed for strings that have 738 or fewer Unicode * code points (not UTF-16 code units). The smallest possible QR Code version is automatically chosen for the output. * The ECC level of the result may be higher than the ecl argument if it can be done without increasing the version. * @param text the text to be encoded, which can be any Unicode string * @param ecl the error correction level to use (will be boosted) * @return a QR Code representing the text * @throws NullPointerException if the text or error correction level is {@code null} * @throws IllegalArgumentException if the text fails to fit in the largest version QR Code, which means it is too long */ public static QrCode encodeText(String text, Ecc ecl) { if (text == null || ecl == null) throw new NullPointerException(); ListThis function allows the user to create a custom sequence of segments that switches * between modes (such as alphanumeric and binary) to encode text more efficiently. This * function is considered to be lower level than simply encoding text or binary data.
* @param segs the segments to encode * @param ecl the error correction level to use (will be boosted) * @return a QR Code representing the segments * @throws NullPointerException if the list of segments, a segment, or the error correction level is {@code null} * @throws IllegalArgumentException if the data is too long to fit in the largest version QR Code at the ECL */ public static QrCode encodeSegments(ListThis function allows the user to create a custom sequence of segments that switches * between modes (such as alphanumeric and binary) to encode text more efficiently. * This function is considered to be lower level than simply encoding text or binary data.
* @param segs the segments to encode * @param ecl the error correction level to use (may be boosted) * @param minVersion the minimum allowed version of the QR symbol (at least 1) * @param maxVersion the maximum allowed version of the QR symbol (at most 40) * @param mask the mask pattern to use, which is either -1 for automatic choice or from 0 to 7 for fixed choice * @param boostEcl increases the error correction level if it can be done without increasing the version number * @return a QR Code representing the segments * @throws NullPointerException if the list of segments, a segment, or the error correction level is {@code null} * @throws IllegalArgumentException if 1 ≤ minVersion ≤ maxVersion ≤ 40 is violated, or if mask * < −1 or mask > 7, or if the data is too long to fit in a QR Code at maxVersion at the ECL */ public static QrCode encodeSegments(ListThis is a cumbersome low-level constructor that should not be invoked directly by the user. * To go one level up, see the {@link #encodeSegments(List,Ecc)} function.
* @param ver the version number to use, which must be in the range 1 to 40, inclusive * @param ecl the error correction level to use * @param dataCodewords the raw binary user data to encode * @param mask the mask pattern to use, which is either -1 for automatic choice or from 0 to 7 for fixed choice * @throws NullPointerException if the byte array or error correction level is {@code null} * @throws IllegalArgumentException if the version or mask value is out of range */ public QrCode(int ver, Ecc ecl, byte[] dataCodewords, int mask) { // Check arguments if (ecl == null) throw new NullPointerException(); if (ver < 1 || ver > 40 || mask < -1 || mask > 7) throw new IllegalArgumentException("Value out of range"); if (dataCodewords == null) throw new NullPointerException(); // Initialize fields version = ver; size = ver * 4 + 17; errorCorrectionLevel = ecl; modules = new boolean[size][size]; // Entirely white grid isFunction = new boolean[size][size]; // Draw function patterns, draw all codewords, do masking drawFunctionPatterns(); byte[] allCodewords = appendErrorCorrection(dataCodewords); drawCodewords(allCodewords); this.mask = handleConstructorMasking(mask); } /** * Creates a new QR Code symbol based on the specified existing object, but with a potentially * different mask pattern. The version, error correction level, codewords, etc. of the newly * created object are all identical to the argument object; only the mask may differ. * @param qr the existing QR Code to copy and modify * @param mask the new mask pattern, 0 to 7 to force a fixed choice or -1 for an automatic choice * @throws NullPointerException if the QR Code is {@code null} * @throws IllegalArgumentException if the mask value is out of range */ public QrCode(QrCode qr, int mask) { // Check arguments if (qr == null) throw new NullPointerException(); if (mask < -1 || mask > 7) throw new IllegalArgumentException("Mask value out of range"); // Copy scalar fields version = qr.version; size = qr.size; errorCorrectionLevel = qr.errorCorrectionLevel; // Handle grid fields isFunction = qr.isFunction; // Shallow copy because the data is read-only modules = qr.modules.clone(); // Deep copy for (int i = 0; i < modules.length; i++) modules[i] = modules[i].clone(); // Handle masking applyMask(qr.mask); // Undo old mask this.mask = handleConstructorMasking(mask); } /*---- Public instance methods ----*/ /** * Returns the color of the module (pixel) at the specified coordinates, which is either 0 for white or 1 for black. The top * left corner has the coordinates (x=0, y=0). If the specified coordinates are out of bounds, then 0 (white) is returned. * @param x the x coordinate, where 0 is the left edge and size−1 is the right edge * @param y the y coordinate, where 0 is the top edge and size−1 is the bottom edge * @return the module's color, which is either 0 (white) or 1 (black) */ public int getModule(int x, int y) { if (0 <= x && x < size && 0 <= y && y < size) return modules[y][x] ? 1 : 0; else return 0; // Infinite white border } /** * Returns a new image object representing this QR Code, with the specified module scale and number * of border modules. For example, the arguments scale=10, border=4 means to pad the QR Code symbol * with 4 white border modules on all four edges, then use 10*10 pixels to represent each module. * The resulting image only contains the hex colors 000000 and FFFFFF. * @param scale the module scale factor, which must be positive * @param border the number of border modules to add, which must be non-negative * @return an image representing this QR Code, with padding and scaling * @throws IllegalArgumentException if the scale or border is out of range */ public BufferedImage toImage(int scale, int border) { if (scale <= 0 || border < 0) throw new IllegalArgumentException("Value out of range"); BufferedImage result = new BufferedImage((size + border * 2) * scale, (size + border * 2) * scale, BufferedImage.TYPE_INT_RGB); for (int y = 0; y < result.getHeight(); y++) { for (int x = 0; x < result.getWidth(); x++) { int val = getModule(x / scale - border, y / scale - border); // 0 or 1 result.setRGB(x, y, val == 1 ? 0x000000 : 0xFFFFFF); } } return result; } /** * Based on the specified number of border modules to add as padding, this returns a * string whose contents represents an SVG XML file that depicts this QR Code symbol. * Note that Unix newlines (\n) are always used, regardless of the platform. * @param border the number of border modules to add, which must be non-negative * @return a string representing this QR Code as an SVG document */ public String toSvgString(int border) { if (border < 0) throw new IllegalArgumentException("Border must be non-negative"); StringBuilder sb = new StringBuilder(); sb.append("\n"); sb.append("\n"); sb.append(String.format("\n"); return sb.toString(); } /*---- Private helper methods for constructor: Drawing function modules ----*/ private void drawFunctionPatterns() { // Draw the horizontal and vertical timing patterns for (int i = 0; i < size; i++) { setFunctionModule(6, i, i % 2 == 0); setFunctionModule(i, 6, i % 2 == 0); } // Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules) drawFinderPattern(3, 3); drawFinderPattern(size - 4, 3); drawFinderPattern(3, size - 4); // Draw the numerous alignment patterns int[] alignPatPos = getAlignmentPatternPositions(version); int numAlign = alignPatPos.length; for (int i = 0; i < numAlign; i++) { for (int j = 0; j < numAlign; j++) { if (i == 0 && j == 0 || i == 0 && j == numAlign - 1 || i == numAlign - 1 && j == 0) continue; // Skip the three finder corners else drawAlignmentPattern(alignPatPos[i], alignPatPos[j]); } } // Draw configuration data drawFormatBits(0); // Dummy mask value; overwritten later in the constructor drawVersion(); } // Draws two copies of the format bits (with its own error correction code) // based on the given mask and this object's error correction level field. private void drawFormatBits(int mask) { // Calculate error correction code and pack bits int data = errorCorrectionLevel.formatBits << 3 | mask; // errCorrLvl is uint2, mask is uint3 int rem = data; for (int i = 0; i < 10; i++) rem = (rem << 1) ^ ((rem >>> 9) * 0x537); data = data << 10 | rem; data ^= 0x5412; // uint15 if (data >>> 15 != 0) throw new AssertionError(); // Draw first copy for (int i = 0; i <= 5; i++) setFunctionModule(8, i, ((data >>> i) & 1) != 0); setFunctionModule(8, 7, ((data >>> 6) & 1) != 0); setFunctionModule(8, 8, ((data >>> 7) & 1) != 0); setFunctionModule(7, 8, ((data >>> 8) & 1) != 0); for (int i = 9; i < 15; i++) setFunctionModule(14 - i, 8, ((data >>> i) & 1) != 0); // Draw second copy for (int i = 0; i <= 7; i++) setFunctionModule(size - 1 - i, 8, ((data >>> i) & 1) != 0); for (int i = 8; i < 15; i++) setFunctionModule(8, size - 15 + i, ((data >>> i) & 1) != 0); setFunctionModule(8, size - 8, true); } // Draws two copies of the version bits (with its own error correction code), // based on this object's version field (which only has an effect for 7 <= version <= 40). private void drawVersion() { if (version < 7) return; // Calculate error correction code and pack bits int rem = version; // version is uint6, in the range [7, 40] for (int i = 0; i < 12; i++) rem = (rem << 1) ^ ((rem >>> 11) * 0x1F25); int data = version << 12 | rem; // uint18 if (data >>> 18 != 0) throw new AssertionError(); // Draw two copies for (int i = 0; i < 18; i++) { boolean bit = ((data >>> i) & 1) != 0; int a = size - 11 + i % 3, b = i / 3; setFunctionModule(a, b, bit); setFunctionModule(b, a, bit); } } // Draws a 9*9 finder pattern including the border separator, with the center module at (x, y). private void drawFinderPattern(int x, int y) { for (int i = -4; i <= 4; i++) { for (int j = -4; j <= 4; j++) { int dist = Math.max(Math.abs(i), Math.abs(j)); // Chebyshev/infinity norm int xx = x + j, yy = y + i; if (0 <= xx && xx < size && 0 <= yy && yy < size) setFunctionModule(xx, yy, dist != 2 && dist != 4); } } } // Draws a 5*5 alignment pattern, with the center module at (x, y). private void drawAlignmentPattern(int x, int y) { for (int i = -2; i <= 2; i++) { for (int j = -2; j <= 2; j++) setFunctionModule(x + j, y + i, Math.max(Math.abs(i), Math.abs(j)) != 1); } } // Sets the color of a module and marks it as a function module. // Only used by the constructor. Coordinates must be in range. private void setFunctionModule(int x, int y, boolean isBlack) { modules[y][x] = isBlack; isFunction[y][x] = true; } /*---- Private helper methods for constructor: Codewords and masking ----*/ // Returns a new byte string representing the given data with the appropriate error correction // codewords appended to it, based on this object's version and error correction level. private byte[] appendErrorCorrection(byte[] data) { if (data.length != getNumDataCodewords(version, errorCorrectionLevel)) throw new IllegalArgumentException(); // Calculate parameter numbers int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[errorCorrectionLevel.ordinal()][version]; int totalEcc = NUM_ERROR_CORRECTION_CODEWORDS[errorCorrectionLevel.ordinal()][version]; if (totalEcc % numBlocks != 0) throw new AssertionError(); int blockEccLen = totalEcc / numBlocks; int numShortBlocks = numBlocks - getNumRawDataModules(version) / 8 % numBlocks; int shortBlockLen = getNumRawDataModules(version) / 8 / numBlocks; // Split data into blocks and append ECC to each block byte[][] blocks = new byte[numBlocks][]; ReedSolomonGenerator rs = new ReedSolomonGenerator(blockEccLen); for (int i = 0, k = 0; i < numBlocks; i++) { byte[] dat = Arrays.copyOfRange(data, k, k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1)); byte[] block = Arrays.copyOf(dat, shortBlockLen + 1); k += dat.length; byte[] ecc = rs.getRemainder(dat); System.arraycopy(ecc, 0, block, block.length - blockEccLen, ecc.length); blocks[i] = block; } // Interleave (not concatenate) the bytes from every block into a single sequence byte[] result = new byte[getNumRawDataModules(version) / 8]; for (int i = 0, k = 0; i < blocks[0].length; i++) { for (int j = 0; j < blocks.length; j++) { // Skip the padding byte in short blocks if (i != shortBlockLen - blockEccLen || j >= numShortBlocks) { result[k] = blocks[j][i]; k++; } } } return result; } // Draws the given sequence of 8-bit codewords (data and error correction) onto the entire // data area of this QR Code symbol. Function modules need to be marked off before this is called. private void drawCodewords(byte[] data) { if (data == null) throw new NullPointerException(); if (data.length != getNumRawDataModules(version) / 8) throw new IllegalArgumentException(); int i = 0; // Bit index into the data // Do the funny zigzag scan for (int right = size - 1; right >= 1; right -= 2) { // Index of right column in each column pair if (right == 6) right = 5; for (int vert = 0; vert < size; vert++) { // Vertical counter for (int j = 0; j < 2; j++) { int x = right - j; // Actual x coordinate boolean upwards = ((right & 2) == 0) ^ (x < 6); int y = upwards ? size - 1 - vert : vert; // Actual y coordinate if (!isFunction[y][x] && i < data.length * 8) { modules[y][x] = ((data[i >>> 3] >>> (7 - (i & 7))) & 1) != 0; i++; } // If there are any remainder bits (0 to 7), they are already // set to 0/false/white when the grid of modules was initialized } } } if (i != data.length * 8) throw new AssertionError(); } // XORs the data modules in this QR Code with the given mask pattern. Due to XOR's mathematical // properties, calling applyMask(m) twice with the same value is equivalent to no change at all. // This means it is possible to apply a mask, undo it, and try another mask. Note that a final // well-formed QR Code symbol needs exactly one mask applied (not zero, not two, etc.). private void applyMask(int mask) { if (mask < 0 || mask > 7) throw new IllegalArgumentException("Mask value out of range"); for (int y = 0; y < size; y++) { for (int x = 0; x < size; x++) { boolean invert; switch (mask) { case 0: invert = (x + y) % 2 == 0; break; case 1: invert = y % 2 == 0; break; case 2: invert = x % 3 == 0; break; case 3: invert = (x + y) % 3 == 0; break; case 4: invert = (x / 3 + y / 2) % 2 == 0; break; case 5: invert = x * y % 2 + x * y % 3 == 0; break; case 6: invert = (x * y % 2 + x * y % 3) % 2 == 0; break; case 7: invert = ((x + y) % 2 + x * y % 3) % 2 == 0; break; default: throw new AssertionError(); } modules[y][x] ^= invert & !isFunction[y][x]; } } } // A messy helper function for the constructors. This QR Code must be in an unmasked state when this // method is called. The given argument is the requested mask, which is -1 for auto or 0 to 7 for fixed. // This method applies and returns the actual mask chosen, from 0 to 7. private int handleConstructorMasking(int mask) { if (mask == -1) { // Automatically choose best mask int minPenalty = Integer.MAX_VALUE; for (int i = 0; i < 8; i++) { drawFormatBits(i); applyMask(i); int penalty = getPenaltyScore(); if (penalty < minPenalty) { mask = i; minPenalty = penalty; } applyMask(i); // Undoes the mask due to XOR } } if (mask < 0 || mask > 7) throw new AssertionError(); drawFormatBits(mask); // Overwrite old format bits applyMask(mask); // Apply the final choice of mask return mask; // The caller shall assign this value to the final-declared field } // Calculates and returns the penalty score based on state of this QR Code's current modules. // This is used by the automatic mask choice algorithm to find the mask pattern that yields the lowest score. private int getPenaltyScore() { int result = 0; // Adjacent modules in row having same color for (int y = 0; y < size; y++) { boolean colorX = modules[y][0]; for (int x = 1, runX = 1; x < size; x++) { if (modules[y][x] != colorX) { colorX = modules[y][x]; runX = 1; } else { runX++; if (runX == 5) result += PENALTY_N1; else if (runX > 5) result++; } } } // Adjacent modules in column having same color for (int x = 0; x < size; x++) { boolean colorY = modules[0][x]; for (int y = 1, runY = 1; y < size; y++) { if (modules[y][x] != colorY) { colorY = modules[y][x]; runY = 1; } else { runY++; if (runY == 5) result += PENALTY_N1; else if (runY > 5) result++; } } } // 2*2 blocks of modules having same color for (int y = 0; y < size - 1; y++) { for (int x = 0; x < size - 1; x++) { boolean color = modules[y][x]; if ( color == modules[y][x + 1] && color == modules[y + 1][x] && color == modules[y + 1][x + 1]) result += PENALTY_N2; } } // Finder-like pattern in rows for (int y = 0; y < size; y++) { for (int x = 0, bits = 0; x < size; x++) { bits = ((bits << 1) & 0x7FF) | (modules[y][x] ? 1 : 0); if (x >= 10 && (bits == 0x05D || bits == 0x5D0)) // Needs 11 bits accumulated result += PENALTY_N3; } } // Finder-like pattern in columns for (int x = 0; x < size; x++) { for (int y = 0, bits = 0; y < size; y++) { bits = ((bits << 1) & 0x7FF) | (modules[y][x] ? 1 : 0); if (y >= 10 && (bits == 0x05D || bits == 0x5D0)) // Needs 11 bits accumulated result += PENALTY_N3; } } // Balance of black and white modules int black = 0; for (boolean[] row : modules) { for (boolean color : row) { if (color) black++; } } int total = size * size; // Find smallest k such that (45-5k)% <= dark/total <= (55+5k)% for (int k = 0; black*20 < (9-k)*total || black*20 > (11+k)*total; k++) result += PENALTY_N4; return result; } /*---- Private static helper functions ----*/ // Returns a set of positions of the alignment patterns in ascending order. These positions are // used on both the x and y axes. Each value in the resulting array is in the range [0, 177). // This stateless pure function could be implemented as table of 40 variable-length lists of unsigned bytes. private static int[] getAlignmentPatternPositions(int ver) { if (ver < 1 || ver > 40) throw new IllegalArgumentException("Version number out of range"); else if (ver == 1) return new int[]{}; else { int numAlign = ver / 7 + 2; int step; if (ver != 32) step = (ver * 4 + numAlign * 2 + 1) / (2 * numAlign - 2) * 2; // ceil((size - 13) / (2*numAlign - 2)) * 2 else // C-C-C-Combo breaker! step = 26; int[] result = new int[numAlign]; int size = ver * 4 + 17; result[0] = 6; for (int i = result.length - 1, pos = size - 7; i >= 1; i--, pos -= step) result[i] = pos; return result; } } // Returns the number of raw data modules (bits) available at the given version number. // These data modules are used for both user data codewords and error correction codewords. // This stateless pure function could be implemented as a 40-entry lookup table. private static int getNumRawDataModules(int ver) { if (ver < 1 || ver > 40) throw new IllegalArgumentException("Version number out of range"); int size = ver * 4 + 17; int result = size * size; // Number of modules in the whole QR symbol square result -= 64 * 3; // Subtract the three finders with separators result -= 15 * 2 + 1; // Subtract the format information and black module result -= (size - 16) * 2; // Subtract the timing patterns // The five lines above are equivalent to: int result = (16 * ver + 128) * ver + 64; if (ver >= 2) { int numAlign = ver / 7 + 2; result -= (numAlign - 1) * (numAlign - 1) * 25; // Subtract alignment patterns not overlapping with timing patterns result -= (numAlign - 2) * 2 * 20; // Subtract alignment patterns that overlap with timing patterns // The two lines above are equivalent to: result -= (25 * numAlign - 10) * numAlign - 55; if (ver >= 7) result -= 18 * 2; // Subtract version information } return result; } // Returns the number of 8-bit data (i.e. not error correction) codewords contained in any // QR Code of the given version number and error correction level, with remainder bits discarded. // This stateless pure function could be implemented as a (40*4)-cell lookup table. static int getNumDataCodewords(int ver, Ecc ecl) { if (ver < 1 || ver > 40) throw new IllegalArgumentException("Version number out of range"); return getNumRawDataModules(ver) / 8 - NUM_ERROR_CORRECTION_CODEWORDS[ecl.ordinal()][ver]; } /*---- Private tables of constants ----*/ // For use in getPenaltyScore(), when evaluating which mask is best. private static final int PENALTY_N1 = 3; private static final int PENALTY_N2 = 3; private static final int PENALTY_N3 = 40; private static final int PENALTY_N4 = 10; private static final short[][] NUM_ERROR_CORRECTION_CODEWORDS = { // Version: (note that index 0 is for padding, and is set to an illegal value) //0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level {-1, 7, 10, 15, 20, 26, 36, 40, 48, 60, 72, 80, 96, 104, 120, 132, 144, 168, 180, 196, 224, 224, 252, 270, 300, 312, 336, 360, 390, 420, 450, 480, 510, 540, 570, 570, 600, 630, 660, 720, 750}, // Low {-1, 10, 16, 26, 36, 48, 64, 72, 88, 110, 130, 150, 176, 198, 216, 240, 280, 308, 338, 364, 416, 442, 476, 504, 560, 588, 644, 700, 728, 784, 812, 868, 924, 980, 1036, 1064, 1120, 1204, 1260, 1316, 1372}, // Medium {-1, 13, 22, 36, 52, 72, 96, 108, 132, 160, 192, 224, 260, 288, 320, 360, 408, 448, 504, 546, 600, 644, 690, 750, 810, 870, 952, 1020, 1050, 1140, 1200, 1290, 1350, 1440, 1530, 1590, 1680, 1770, 1860, 1950, 2040}, // Quartile {-1, 17, 28, 44, 64, 88, 112, 130, 156, 192, 224, 264, 308, 352, 384, 432, 480, 532, 588, 650, 700, 750, 816, 900, 960, 1050, 1110, 1200, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2100, 2220, 2310, 2430}, // High }; private static final byte[][] NUM_ERROR_CORRECTION_BLOCKS = { // Version: (note that index 0 is for padding, and is set to an illegal value) //0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level {-1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 8, 8, 9, 9, 10, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 24, 25}, // Low {-1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 35, 37, 38, 40, 43, 45, 47, 49}, // Medium {-1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 12, 16, 12, 17, 16, 18, 21, 20, 23, 23, 25, 27, 29, 34, 34, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 62, 65, 68}, // Quartile {-1, 1, 1, 2, 4, 4, 4, 5, 6, 8, 8, 11, 11, 16, 16, 18, 16, 19, 21, 25, 25, 25, 34, 30, 32, 35, 37, 40, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 77, 81}, // High }; /*---- Public helper enumeration ----*/ /** * Represents the error correction level used in a QR Code symbol. */ public enum Ecc { // These enum constants must be declared in ascending order of error protection, // for the sake of the implicit ordinal() method and values() function. LOW(1), MEDIUM(0), QUARTILE(3), HIGH(2); // In the range 0 to 3 (unsigned 2-bit integer). final int formatBits; // Constructor. private Ecc(int fb) { formatBits = fb; } } /*---- Private helper class ----*/ /** * Computes the Reed-Solomon error correction codewords for a sequence of data codewords * at a given degree. Objects are immutable, and the state only depends on the degree. * This class exists because the divisor polynomial does not need to be recalculated for every input. */ private static final class ReedSolomonGenerator { /*-- Immutable field --*/ // Coefficients of the divisor polynomial, stored from highest to lowest power, excluding the leading term which // is always 1. For example the polynomial x^3 + 255x^2 + 8x + 93 is stored as the uint8 array {255, 8, 93}. private final byte[] coefficients; /*-- Constructor --*/ /** * Creates a Reed-Solomon ECC generator for the specified degree. This could be implemented * as a lookup table over all possible parameter values, instead of as an algorithm. * @param degree the divisor polynomial degree, which must be between 1 and 255 * @throws IllegalArgumentException if degree < 1 or degree > 255 */ public ReedSolomonGenerator(int degree) { if (degree < 1 || degree > 255) throw new IllegalArgumentException("Degree out of range"); // Start with the monomial x^0 coefficients = new byte[degree]; coefficients[degree - 1] = 1; // Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}), // drop the highest term, and store the rest of the coefficients in order of descending powers. // Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D). int root = 1; for (int i = 0; i < degree; i++) { // Multiply the current product by (x - r^i) for (int j = 0; j < coefficients.length; j++) { coefficients[j] = (byte)multiply(coefficients[j] & 0xFF, root); if (j + 1 < coefficients.length) coefficients[j] ^= coefficients[j + 1]; } root = (root << 1) ^ ((root >>> 7) * 0x11D); // Multiply by 0x02 mod GF(2^8/0x11D) } } /*-- Method --*/ /** * Computes and returns the Reed-Solomon error correction codewords for the specified sequence of data codewords. * The returned object is always a new byte array. This method does not alter this object's state (because it is immutable). * @param data the sequence of data codewords * @return the Reed-Solomon error correction codewords * @throws NullPointerException if the data is {@code null} */ public byte[] getRemainder(byte[] data) { if (data == null) throw new NullPointerException(); // Compute the remainder by performing polynomial division byte[] result = new byte[coefficients.length]; for (byte b : data) { int factor = (b ^ result[0]) & 0xFF; System.arraycopy(result, 1, result, 0, result.length - 1); result[result.length - 1] = 0; for (int i = 0; i < result.length; i++) result[i] ^= multiply(coefficients[i] & 0xFF, factor); } return result; } /*-- Static function --*/ // Returns the product of the two given field elements modulo GF(2^8/0x11D). The arguments and result // are unsigned 8-bit integers. This could be implemented as a lookup table of 256*256 entries of uint8. private static int multiply(int x, int y) { if (x >>> 8 != 0 || y >>> 8 != 0) throw new IllegalArgumentException("Byte out of range"); // Russian peasant multiplication int z = 0; for (int i = 7; i >= 0; i--) { z = (z << 1) ^ ((z >>> 7) * 0x11D); z ^= ((y >>> i) & 1) * x; } if (z >>> 8 != 0) throw new AssertionError(); return z; } } }